We consider a multihop distributed uplink reception system in which $K$ users transmit independent messages to one data center of $N_{\rm r} \geq K$ receive antennas, with the aid of multihop intermediate relays. In particular, each antenna of the data center is equipped with one-bit analog-to-digital converts (ADCs) for the sake of power-efficiency. In this system, it is extremely challenging to develop a low-complexity detector due to the non-linearity of an end-to-end channel transfer function (created by relays' operations and one-bit ADCs). Furthermore, there is no efficient way to estimate such complex function with a limited number of training data. Motivated by this, we propose a supervised-learning (SL) detector by introducing a novel Bernoulli-like model in which training data is directly used to design a detector rather than estimating a channel transfer function. It is shown that the proposed SL detector outperforms the existing SL detectors based on Gaussian model for one-bit quantized (binary observation) systems. Furthermore, we significantly reduce the complexity of the proposed SL detector using the fast kNN algorithm. Simulation results demonstrate that the proposed SL detector can yield an attractive performance with a significantly lower complexity.